Power densities modelling

Spectral discrimination (9) and specific gas detection can be modeled if one assumes the gas absorbs photons of a specific wavelength exponentially with distance into the gas (Beet s law). When the absorption distance is x (cm), the incident it power density at the detector in the spectral band pass is J (W/cm ) and the power density incident on the gas is the gas concentration, C (ppm) is given by ... 

The processes in a cooling system of electronic devices with high power density can be modeled as follows. The coolant with temperature T2.0 and pressure F2.0 enters into the micro-channel from the tank (5) (Fig. 10.2). The mass capacity of the liquid in the tank (5) is large enough, therefore the heat flux from the micro-channel... 

A coal slurry is to be transported by pipeline. It has been determined that the slurry may be described by the power law model, with a flow index of 0.4, an apparent viscosity of 50 cP at a shear rate of 100 s-1, and a density of 90 lbm/ft3. What horsepower would be required to pump the slurry at a rate of 900 gpm through an 8 in. sch 40 pipe that is 50 mi long ... 

In contrast to battery technology, ultra thin electrodes cannot provide an increase in SC power density. Our theoretical model shows an optimum electrode thickness to exist in the range of 50-150 pm, the exact value depending on the porosity and nature of the electrode material. 

On the other hand, the total heating power can be calculated as the product of heating voltage, Vheat. and heating current, 4eaf For a heater occupying an area, Aheat. in the geometric model, the power density can be calculated to ... 

The focus of this evaluation is on the results that were reported using four different resins [52] PC resin, LLDPE resin, EAA copolymer, and an LDPE resin. The shear viscosities for the resins at selected processing temperatures are shown in Pig. 7.17 and were modeled using the power law model provided by Eq. 7.42. The parameters for the model are given in Table 7.3. As shown in Pig. 7.17 and the n values in Table 7.3, the PC resin shear-thinned the least while the EDPE resin shear-thinned the most. The LLDPE and EAA resins have n values between those for the PC and LDPE resins. The melt density for the LDPE and LLDPE resins at 240 °C is 735 kg/mT The melt density of the EAA resin at 220 °C was 785 kg/m and the melt density of the PC resin at 280 °C was 1073 kg/mT... 

Ultrasonic irradiation of aqueous solutions of the chlorophenols was carried out with a Vibra Cell Model VC-250 direct immersion ultrasonic horn (Sonics Materials Newtown, CT) operated at a frequency of 20 kHz with a constant power output of 50 W (the actual insonation power at the solution was 49.5 W, and the power density was 52.1 W/cm2). Reactions were done in a glass sonication cell (4.4 cm i.d. by 10 cm), similar to the one described by Suslick (1988). The temporal course of the sonochemical processes was monitored by HPLC. 

This design is still under preliminary modeling and testing. Research is focused on the further improvement of the power density, avoiding the use of high temperature seals. 

These results led us to analyze the relationship between carrier-wave frequency and power density. We developed a mathematical model (6) which takes into account the changes in complex permittivity of brain tissue with frequency. This model predicted that a given electric-field intensity within a brain-tissue sample occurred at different exposure levels for 50-, 147-, and 450-MHz radiation. Using the calculated electric-field intensities in the sample as the independent variable, the model demonstrated that the RF-induced calcium-ion efflux results at one carrier frequency corresponded to those at the other frequencies for both positive and negative findings. In this paper, we present two additional experiments using 147-MHz radiation which further test both negative and positive predictions of this model. 

Figure 2 displays the percent difference in mean efflux between the exposed and sham groups at different power densities of 50- and 147-MHz radiation, as well as lines connecting those power densities which would produce the same value of internal electric field intensity in the samples. These results support the mathematical model and demonstrate its usefulness in defining effective power densities over a range of carrier frequencies. 

Table I and Figure 3 highlight another intriguing feature of the results obtained to date. The experimental results at 50 and 147 MHz have demonstrated two effective power density ranges separated and bracketed by regions of no effect. The mathematical model, applied to this data, predicts an additional effective power density range at each carrier frequency. Moreover, if the experimental results of Adey (1 1) are evaluated in this manner, a fourth effective power density window is predicted for each of the carrier frequencies. Confirmation of the predictions of the mathematical model resulting from these data is necessary in order to ensure that these results reflect a true response of the biological tissue.

Keeping the average electric field intensity the same within a spherical model of chick-brain in buffer solution at different incident carrier wave frequencies requires that incident power density be changed with frequency to compensate for the change in complex permittivity and wavelength with frequency. The resulting Equations (3) and (A) relate corresponding values of P. at carrier frequencies of 50, 1A7, and A50 MHz. 1... 

---